Question

Write an equation in slope-intercept form of a line passing through the given point andperpendicular to the given line.18. (3,0);x-y=4

Answer 1

18)

The given equation is

x - y = 4

It passes through the point (3, 0)

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept

We would rewrite the given equation like the slope intercept equation. we have

x - y = 4

Adding y to both sides of the equation, we have

x - y + y = 4 + y

x = 4 + y

subtracting 4 from both sides,

x - 4 = 4 - 4 + y

x - 4 = y

y = x - 4

By comparing this equation with the slope intercept equation,

m = 1

c = - 4

If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. This means that the slope of the perpendicular line passing through (3, 0) is - 1/1 = - 1

m = - 1

We would find the y intercept of the line by substituting m = - 1, x = 3 and

y = 0 into the slope intercept equation. We have

0 = - 1 * 3 + c

0 = - 3 + c

c = 0 + 3

c = 3

By substituting m = - 1 and c = 3 into the slope intercept equation, the equation of the perpendicular line is

y = - x + 3